Gypsum dunes at White Sands National Monument, New Mexico, provide an excellent analog to sulfate-rich eolian outcrops on Meridiani Planum, Mars, as characterized by the Rover Opportunity. Numerous outcrops imaged by Opportunity contain polygonal cracks that crosscut bedding and extend across most surfaces of boulders. Some of these cracks are associated with millimeter-thick platy fins that protrude as much as a few centimeters above outcrops. Similar cracks crosscut bedding at White Sands on erosional stoss slopes and in pedestals of cemented dune sand. The cracks at White Sands form in response to cementation of damp gypsum sand followed by contraction due to dehydration. During warm seasons, cracked sand is dry and cracks rarely grow, although some may form after rainstorms. Two types of fins form along cracks and differentially eroded laminae. White fins represent subsurface differential cementation along cracks followed by differential erosion. Tan fins form due to cementation of crack edges and laminae on exposed dune surfaces. Wind-blown sediment adheres to damp tan fins. Similar processes may be important for crack and fin formation in Meridiani Planum outcrops, implying recent water cycling between sulfate outcrops and the Martian atmosphere.